SIMULATION STUDY OF A DYNAMIC AGV-CONTAINER JOB DEPLOYMENT SCHEME

Transcription

1 1 SIMULATION STUDY OF A DYNAMIC AGV-CONTAINER JOB DEPLOYMENT SCHEME By Cheng Yong Leong B.Eng. Electrical Engineering National University of Singapore, 2000 SUBMITTED TO THE SMA OFFICE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN HIGH PERFORMANCE COMPUT ATION FOR ENGINEERED SYSTEMS AT THE SINGAPORE-MIT ALLIANCE JUNE 2001 Signature of Author: Cheng Yong Leong High Performance Computation for Engineered Systems June 30, 2001 Certified by: Assoc. Prof. Teo Chung Piaw SMA HPCES Fellow Project Supervisor Accepted by: Assoc. Prof. Khoo Boo Cheong Programme Co-Chair HPCES Programme Accepted by: Prof. Jaime Peraire Programme Co-Chair HPCES Programme

2 2 ACKNOWLEDGEMENTS The author will wish to thank his advisor Prof. Teo Chung Piaw whose expert advice has helped in the completion of the project. His guidance and comments has aided in looking into the finer aspects of the simulation and in obtaining meaningful results. The author will wish to thank Mr. Loy Hein Thuan, Manager, Operations Planning Department, PSA Corp., for providing the opportunity to work on this problem. The author is grateful to PSA Corp for providing the resources to do the simulation work. The author will also wish to thank Dr. Tan Kok Choon, Manager, Operations Planning Department, PSA Corp. for providing the author with advice for this problem. The author will like to thank the PSA Corp. AGV team comprising of Mr. Lee Tat Wee, Senior Systems Analyst, Container Terminal Systems Department, Mr. Ricky Seng Siang Ping, Senior Operations Research Officer, Operations Planning Department and Mr. Gabriel Lau, Deputy Manager (Ship Operations Systems), Container Terminal Systems Department for proposing this project. The author will also wish to thank SMA for the support in doing this project. Last but not the least the author will like to thank all the SMA students, which make the stay in SMA more memorable. Author 15th June 2001

3 3 TABLE OF C ONTENTS 1 INTRODUCTION BACKGROUND OF CONTAINER TERMINAL OPERATION AUTOMATED GUIDED VEHICLES (AGV S) PSA PORT AUTOMATION PROJECT (PPAP) PROBLEM STATEMENT PROJECT CONTRIBUTION OUTLINE OF THE THESIS LITERATURE REVIEW CURRENT DEPLOYMENT SCHEME THEORETICAL INSIGHT BEHIND PMDS DESIGN OF THE PMDS MODEL PROPOSED DEPLOYMENT SCHEME PROBLEM FORMULATION OF THE PROPOSED DEPLOYMENT SCHEME Calculation of Non-zero Arc Costs Arc cost of arcs flowing from AGV to container node Arc cost of arcs flowing from container i to container j node DESIGN OF THE PROPOSED DEPLOYMENT SCHEME MODEL DEADLOCK PREDICTION & AVOIDANCE ALGORITHM THE CONDITIONS LEADING TO A DEADLOCK TYPES OF DEADLOCK IN THE AGVS METHODS IN PREDICTING OR DETECTING CYCLIC DEADLOCK PROPOSED DEADLOCK PREDICTION STRATEGY PROPOSED DEADLOCK AVOIDANCE STRATEGY One-zone step deadlock resolution IMPLEMENTATION AUTOMOD SIMULATION SOFTWA RE SPECIFICATIONS OF THE TWO MODELS DETERMINATION OF THE EXPECTED VALUES OF AVERAGE VELOCITY OF THE VEHICLES C-CODES AND INTERFACING RESULTS AND DISCUSSION...44

4 4 7.1 SCHEMATICS OF THE SIMULATION MODEL LAYOUT COMPARISON OF EFFECTS OF THE NUMBER OF AGVS EFFECT OF THE VARIATION OF TIME WINDOW DISCUSSIONS AND CONCLUSIONS REFERENCES APPENDIX A MINIMUM COST FLOW (MCF) CODE... 54

5 5 L IST OF FIGURES Figure 1.1: A prototype of AGV used by PSA Corp Figure 1.2:Part of the PSA simulation model showing routing on one berth Figure 3.1:Illustration of a typical schedule of job deployment Figure 3.2:Illustration of the selection of an AGV to dispatch a job Figure 3.3:An example of the assignment of the appointed pickup/drop off time for 8 jobs Figure 3.4:A visualization of the current deployment scheme Figure 4.1:Example of a network of 2 AGVs and 4 containers using formulation (N1) Figure 4.2:Example of a network of 2 AGVs and 4 containers using formulation (N2) Figure 4.3:Illustration of the calculation of the distance traveled for the 4 cases Figure 4.4: An assignment example of appointed time for 10 jobs for 1 crane Figure 5.1:A cyclic deadlock formed by the vehicles Figure 5.2:Flowchart of the one-zone step deadlock prediction algorithm Figure 5.3: Illustration of one-zone step deadlock prediction Figure 6.1: Illustration of the C interface with the AutoMod model for the mcf model Figure 7.1: Layout of the four berths in the simulation model Figure 7.2:Scenarios showing AGVs picking/dropping jobs in the berth and yard areas... 44

6 6 L IST OF TABLES Table 6.1: List of average velocities of random selection of 10 AGVs Table 6.2:Average velocity for the total number of AGVs used Table 7.1:Total number of boxes serviced in each berth Table 7.2:Ship average makespan in hours in each berth for pmds model Table 7.3:Ship average makespan in hours in each berth for mcf model Table 7.4:Average throughput of the ship in each berth for pmds model Table 7.5:Average throughput of the ship in each berth for mcf model Table 7.6: Length of time deviations from the appointed service time for pmds model Table 7.7:Length of time deviations from the appointed service time for mcf model 47 Table 7.8: Improvement of the mean time deviations of mcf model Table 7.9: Total number of boxes serviced in each berth Table 7.10:Ship average makespan in each berth for pmds model Table 7.11:Ship average makespan in each berth for mcf model Table 7.12:Average throughput of the ship in each berth for pmds model Table 7.13:Average throughput of the ship in each berth for mcf model Table 7.14:Length of time deviations from the appointed service time for pmds model... 49

7 7 SIMULATION STUDY OF A DYNAMIC AGV-CONTAINER JOB DEPLOYMENT SCHEME by Cheng Yong Leong Submitted to the SMA office on June 15, 2001 In Partial Fulfillment of the Requirements for the Degree of Master of Science in High Performance Computation for Engineered Systems ABSTRACT Automated Guided Vehicle (AGV) Container-Job deployment is essentially a vehicle - dispatching problem. In this problem, the impact of vehicle dispatching polices on the ship makespan for discharging and/or loading operations is analyzed. In particular, here the storage location of each container is an input to the simulation model and is known. Thus, given a storage location for each container to be discharged from the ship and given the current location of each container to be loaded onto the ship, the problem is how to dispatch vehicles to containers so as to minimize the makespan of the ship so as to increase the throughput. The makespan of the ship refers to the time a ship spends at the port for loading and unloading operations. Automated Guided Vehicle System (AGVS) forms a very important part of automated material handling and its performance affects the efficiency of the entire system. Deadlock formation is a serious problem as it stalls the AGVS. Thus, the objective of this project is to develop an efficient deployment algorithm scheme, which will incorporate and integrate with the deadlock prediction and avoidance algorithm done in previous study [1]. The prediction & avoidance algorithm aims to predict and avoid cyclic deadlock. This project will compare the performance of current deployment scheme used by PSA with the new proposed deployment scheme, both with deadlock prediction & avoidance algorithm. The current deployment scheme, namely PMDS makes use of a greedy heuristics which dispatches the available vehicle that will reach the quay with the minimum amount of time the vehicle has to spend waiting for the crane to discharge or load the container from or onto the ship. The new deployment scheme

8 8 aims to formulate the problem as a minimum cost flow problem, which will then be solved by network simplex code. The vehicles will then be dispatched based on the solutions obtained. The two simulation models are implemented using discrete-event simulation software, AutoMod, and the performances of both deployment schemes are analyzed. The simulation results show that the new deployment scheme will result in a higher throughput and lower ship makespan than the current deployment scheme. Keywords: Automated Guided Vehicles (AGV), greedy heuristic, minimum cost flow, network formulations, simulation study, deadlocks, one-zone step deadlock prediction and avoidance algorithm, vehicle deployment, job based approach, vehicle based approach Dissertation Supervisors: 1. Assoc. Prof. Teo Chung Piaw, SMA Fellow, NUS 2. Dr. Tan Kok Choon

9 Chapter 1 Introduction 9 1 INTRODUCTION In 1966, the first deep-sea container service was introduced for the transport of general cargo. Since then, container shipping has become a common way to move all types of products, especially high-value cargo. Due to decreased costs and lower rates, customer demand, increasingly cost-efficient processes, and globalization of trade, the use of containers for sea-borne cargo has seen a steady increase since its introduction in the mid 1960 s. Container terminals have become an important component of logistics networks. To satisfy demand of customers, it is necessary that container ships are unloaded and loaded quickly. This needs the development of sophisticated, highly automated container transportation systems, which will allow the efficient container movement within the container terminal area. One of the world s leading port operators, PSA Corporation based in Singapore, is planning to automate its container transportation within the container terminal by implementing an Automated Guided Vehicle (AGV) System (AGVS) in its new, highly automated container terminal. Typical operational planning and control problems in such system are: dispatching of AGVs to containers in the terminal, routing of AGVs and controlling traffic in the network of lanes and junctions. In this project, we consider one aspect of the terminal operation, which is to dispatch AGVs to containers in the terminal. 1.1 BACKGROUND OF CONTAINER TERMINAL OPERATION When a vessel arrives at the container terminal for a transshipment operation, containers are first discharged from the vessel onto AGVs by quay cranes; the AGVs then transport the containers to the pre-specified storage locations in the yard area. Typically, after most, or all, containers have been unloaded from the vessel, other containers are uploaded onto the ship. These containers are carried by AGVs from the yard to the quay area, and are loaded onto the ship by quay crane. There are two types of cranes in the terminal: quay cranes, which used to load and unload containers to

10 Chapter 1 Introduction 10 and from the ship; and yard crane, used to load and unload containers at the terminal yard storage area. Containers handled by the terminals are in standard size (Twenty-foot-equivalent unit (TEU)) containers. An AGV can carry one TEU or two TEUs. When a container is unloaded from a vessel, it is pickup by a quay crane and drop onto an AGV directly without unloading it onto the ground. Unloading containers onto ground will need additional crane operation to lift it from the ground and load onto the AGV, which will affect the throughput of the whole operation and is not desirable. Thus, an AGV needs to be available by the crane throughout the loading and unloading operations. A few hours before the arrival of an incoming ship, the terminal receives detail information about its contents; i.e., number and location of containers that are to be discharged into the yard, and a list of containers the have to be uploaded onto the vessel. This information allows the terminal dispatchers to generate a crane job sequence, which specify the orders of the containers that are going to be unloaded from and loaded onto the vessel by each quay crane serving the vessel. The unloading sequence to unload containers from vessel onto the yard is determined by the position of the containers on the vessel, their destinations and contents. Similarly, the uploading sequence to upload containers from the yard to the vessel depends on the content, location and next destination of the containers. The crane job sequence always starts with discharging containers from vessel, followed by the loading containers onto the vessel. From these crane job sequences, each container is given a time window that it must leave its source and reach its destination determined by the working rate of the crane that serve this container. 1.2 AUTOMATED GUIDED VEHICLES (AGVS) AGVs are driver-less industrial trucks, usually powered by electric motors and batteries. AGVs range in size from carrying small loads of a few kilograms up to loads over 100 tons. The working environment may vary from offices with carpet floor to harbor dockside areas. A prototype of AGV used by PSA Corp. in its highly automated container terminal is shown in Figure 1.1.

11 Chapter 1 Introduction 11 Figure 1.1: A prototype of AGV used by PSA Corp. Modern AGV Systems are now controlled by flexible, on-board microcomputers. System management computers and radio frequency controls are incorporated into the system to optimizing the AGV utilization, giving transport orders, tracking the material in transfer and directing the AGV traffic. Through these advance control systems, the exact location of AGV, speed of AGV and the traffic condition at certain zone are known from time to time. Under this ideal information system, a more efficient dispatching, routing and traffic control strategy could be implemented. 1.3 PSA PORT AUTOMATION PROJECT (PPAP) PSA Corporation is one of the world s leading port operators and in Singapore PSA handles more than 17 Million TEU of cargo in the year of PSA operate many ports outside Singapore and due to increasing demand and also to maintain and improve their quality of service, they resort to automation of port activities. Currently, PSA employs fully automated cranes in their ports as part of their container storageretrieval system. It operates about 24 quay cranes, 44 bridge cranes (which are yard cranes) and 15 gantry cranes at the Pasir Panjang Terminal. To further improve the service, PSA wants to fully automate their port operation. As part of this automation process, AGV system is introduced to transport containers within port. In Singapore, land is a scarce resource and efficient usage of the available space is one the prime objective in any project. An important feature of the ports in

12 Chapter 1 Introduction 12 Singapore is that most of the cargo (almost 80%) is for transshipment. Hence, a sufficient amount of space for transshipment goods must be available close to the dock. Yard Side lanes Traveling lane Working lane 1 Corridor Working lane 2 Container Storage Area Berth lanes Side Figure 1.2:Part of the PSA simulation model showing routing on one berth. To maximize the usage of the land area close to the dock, a complex AGVS layout has been planed for PSA. A part of the layout drawn by PSA is shown in Figure 1.2. The Export/Import containers are stored in the storage yard and the vessels arrive at the berth. All the containers need to be transported to or from vessel and hence there are more lanes in the berth-side. The transshipment containers are stored in the storage yard. A berth is the area between the two corridors. When the layout is complex, the control and navigation systems of the AGVS must be very efficient to deploy AGV to container jobs in the terminal, and prevent any major congestion in the AGV traffic. 1.4 PROBLEM STATEMENT To design a highly efficient automated container terminal, PSA expressed the need to develop a dynamic AGV dispatching strategy to deploy AGVs to transport containers within the terminal area.

13 Chapter 1 Introduction 13 The AGV used by PSA has capacity to carry one 40/45 feet container or one 20 feet container or two 20 feet containers. Each container job involves the loading of a container onto the AGV, the movement of the AGV to the destination of the container, and the unloading of the container from the AGV. The following assumptions are used in this project: Exact location and impending movement route of an AGV can be accurately retrieved from the AGV Deployment System (ADS). Time needed to travel from each point to another point in the AGVS can be retrieved from the ADS. Source and destination location of all container jobs are given. The time for the unloading container (container to be unloaded from a vessel) to leave the quay crane is generated and given. The time for a loading container (container to be loaded onto a vessel) to reach the quay crane is generated and given. Yard crane resources are always available. The AGV dispatching problem is to deploy AGVs to serve all the container jobs such that all the time constraints for all jobs are met. This makes sure that an AGV has to reach the quay crane before the time the container is to be dropped off or picked up by the quay crane. If this constraint is satisfied by the deployment scheme, the terminal is operated at a throughput rate that is pre-specified. However, the queuing of AGVs to queue at the quayside is undesirable as it creates congestion at the quayside, hence another objective of the deployment scheme is to reduce the waiting time of the AGVs at the quayside when they are waiting for the quay crane to pickup or drop off containers onto it. Although an AGV can carry either one or two containers, only the case that an AGV can only carry one container at a time will be studied in the simulation. The project should propose a more optimal deployment scheme for this simulation model and compare the performance of the two deployment schemes.

14 Chapter 1 Introduction PROJECT CONTRIBUTION The problem proposed has been studied in detail and the following chapters provide a detailed description of the problem and the solution proposed. The highlights of the project are: Development of an efficient model using a simulation language, AutoMod. Development of the current model using a simulation language, AutoMod. Solving of this model using minimum cost flow algorithm. Integration of both deployment schemes with deadlock prediction and avoidance strategy. 1.6 OUTLINE OF THE THESIS The remainder of the document is divided into the following chapters. Chapter 2 provides a detailed review of the existing literature on vehicle dispatching using evolutionary algorithm, vehicle dispatching in Flexible Manufacturing System, vehicle-scheduling algorithms. Chapter 3 presents a discussion on the design of the current deployment scheme adopted by PSA. Chapter 4 presents a discussion on the design of the proposed deployment scheme developed using minimum-cost flow algorithm. Chapter 5 presents the deadlock prediction and avoidance measures adopted. In Chapter 6, a detail description of the implementation of the model in AutoMod is provided Chapter 7 provides results obtained in the project and a detail discussion of the results is included.

15 Chapter 2 Literature Review 15 2 LITERATURE REVIEW Vehicle dispatching strategy is a very important research topic that has been extensively analyzed, mainly in the context of Material Handling System (MHS) control. The majority of these efforts have been centered on Automated Guided Vehicle Systems. Co [15] dealt with the assignment of transportation equipment to service requests on the shop floor. He assumed a fixed shop layout with predetermined material handling flow paths and fixed transporter fleet size. The problem can be viewed as a vehiclescheduling problem and can be modeled using Mixed Integer Programming. The problem is also similar to the Time Constrained Vehicle Routing Problem (TCVRP) which is proven to be NP-hard. Egbelu and Tanchoco [17] presented some heuristic rules for dispatching AGVs in a job shop environment. There are two main approaches to the problem: job-based approach and vehicle-based approach. The job-based approach tries to schedule the tightly constrained jobs (i.e. with smaller time windows) first. The approach entails selecting the Nearest Vehicle (NV), the Farthest Vehicle (FV), the Longest Idle Vehicle (LIV) or the Least Utilized Vehicle (LUV) to serve the most tightly constrained job. The unloaded movement times of vehicles, which correspond to the sequence dependent set-up times in the scheduling framework, are ignored. The vehicle-based approach, on the other hand tries to minimize the unloaded travel times so that jobs will have more opportunities to be scheduled. Examples of vehicle-based approaches are Shortest Travel Time (STT), Longest Travel Time (LTT), Maximum Outgoing Queue Size (MOQS), Minimum Remaining Outgoing Queue Space (MROQS) and First Come First Serve (FCFS) Simchi-Levi et al [3] proposed a vehicle-based dispatching strategy for a mega container terminal. The objective was to minimize the makespan to serve a vessel.

16 Chapter 2 Literature Review 16 The heuristic proposed deploying vehicles to the earliest possible container jobs once the vehicle is free. The deviation of the proposed heuristic makespan from optimality was also investigated. Akturk and Yilmaz [18] proposed an algorithm to schedule vehicles and jobs in a decision-making hierarchy based on mixed integer programming. Their microopportunistic scheduling algorithm (MOSA), combined job-based and vehicle-based approaches into a single algorithm in which critical jobs and travel times of unloaded vehicles are considered simultaneously. However, MOSA is only useful for AGV systems with a small number of jobs and vehicles as the computational time becomes impractical when the job number or the size of the vehicle fleet is large. A human dispatcher typically performs the assigning of vehicles to jobs. Successful performance of this task requires much experience, judgment and expertise on the part of the scheduler. Hence, Potvin et al [16] suggested the use of a neural network model as a sub-symbolic and empirical means of modeling the decision process of expert dispatchers. As an alternative to using expert systems, Bose et al [19] proposed obtaining an initial solution using either a job-based or vehicle-based approach and subsequently improving it via an evolutionary algorithm. However, these algorithms only perform well for AGV systems with small numbers of jobs and vehicles. Majority of the above literatures assumed a unit capacity vehicle, which could only take one unit of load at a time. An efficient way to solve a unit capacity vehicle - dispatching problem is to first formulate the whole deployment problem as a network flow problem. A network simplex algorithm with an upper bound technique, which is a specialized revised simplex algorithm, can solve the problem efficiently by exploiting the structure of the network flow problem. The linear algebra of the simplex algorithm is replaced by simple network operations. Ahuja, Magnanti, and Orlin [9] describe the (primal) network simplex algorithm and gave pseudo-codes and implementation details. An implementation of the primal and dual network simplex algorithm is presented by Löbel in [13]. In practical applications, besides the vehicle-dispatching problem one must also consider the possible formation of deadlocks in the Automated Guided Vehicle

17 Chapter 2 Literature Review 17 System. The deadlock detection and avoidance strategy that has been used in this project is based on the new approach proposed by Wee and Moorthy [1]. The deadlock prediction is a one-zone step prediction algorithm. The avoidance strategy makes use of the wait and proceed approach and the semi-dynamic re-routing strategy, which uses the shortest path algorithm to determine the routes for the AGVs. To evaluate the performance of the deployment schemes, simulation studies are essential. To implement the simulation effectively, prudent steps must be taken to ensure the accuracy of the results presented by the model. A systematic approach to a proper simulation study has been discussed by Banks and Carson in [11] and Law in [12].

18 Chapter 3 Current Deployment Scheme 18 3 CURRENT DEPLOYMENT SCHEME The current deployment scheme, namely the Prime-Mover Deployment scheme (PMDS), as the name suggests, is derived from the original prime mover deployment scheme which is going to be incorporated into the AGVS where the man-driven prime mover is going to be replaced by the Automated Guided Vehicle (AGV). Each container corresponding to a ship is a job and there are 2 types of job movements, discharging/unloading (movement from quay to yard) and loading (movement from yard to quay). We assume that we are given the crane job sequence for each quay crane serving the ship. The crane job sequence for each quay crane consists of the following information. A sequence of jobs that will be discharged from/loaded onto the ship, A set of potential storage locations in the yard area for each container to be discharged from the ship and is already determined. The job s pickup location is denoted as the source of the container to be loaded onto the vehicle and the job s drop off location is denoted as the destination of the container to be unloaded from the vehicle. In this chapter, the insight and the algorithm behind the PMDS model will be discussed 3.1 THEORETICAL INSIGHT BEHIND PMDS The general rule behind the deployment scheme is based on a greedy heuristic that aims to dispatch vehicles to jobs such that the time each vehicle spends waiting for the quay crane to serve a job is minimized. For each quay crane, the predetermined crane job sequence, consisting of n jobs may consist of only unloading jobs (or u job) or only loading jobs (or l job) or a combination of both unloading and loading jobs (or u/l job). In the latter case, the job sequence consists of two parts: the first part includes all the u jobs followed by all the l jobs. For each u ( l ) job, there is a predetermined drop-off (pickup) point in the yard, which is the location of the job.

19 Chapter 3 Current Deployment Scheme 19 In the greedy heuristic, the first k jobs are assigned, each to a single AGV. The next job is assigned to the AGV such that the AGV will reach the location at a time that will minimize the AGV waiting time for the crane to unload/load the u / l job to the vehicle. Specifically, when assigning a u job, the AGV that has the closest arrival time at the quayside to the appointed pickup time of the job will be dispatched to this job. Similarly, when assigning a l job, the AGV that has the closest arrival time at the quayside to the appointed drop off time of the job will be dispatched to this job. Normally for l job, the AGV that can reach the job source at the yardside at the earliest time is dispatched since it needs to travel a longer distance from current position to the yardside and to the quayside compared to a u job. The deployment scheme focuses on deployment of one job at a time. All the jobs are arranged in the order of First In First Out (FIFO) basis based on the earliest appointed pickup/drop off time of the job at the quayside. A pictorial view of the job schedule is shown in Figure 3.1. Current time Time window Select first Job to dispatch Time Estimated travel time to destination Job 0 Job 1 Job 2 Slack/ waiting time Planned job appointed time Job 3 Planned job finished time Actual job start time Actual job finished time Figure 3.1:Illustration of a typical schedule of job deployment From Figure 3.1, Job 0 with the earliest appointed pickup/drop off time or the least waiting time (indicated in dotted arrow) will be selected to dispatch first followed by Job 1,2,3 and so on. The length of the time window dictates the time interval between the appointed pickup/drop off times of two jobs. If the job is a u job, the start time will be the pickup time and if a job is a l job, the start time will be the drop off time. A pictorial view of the selection of a vehicle for deployment is shown in Figure 3.2.

20 Chapter 3 Current Deployment Scheme 20 Select a vehicle to dispatch Job i Job i appointed pickup/drop off time Time AGV 0 AGV 1 AGV. 2 AGV 3 AGV 4 AGV 5 Estimated travel time to quay AGV available time Waiting time AGV estimated arrival time at the quay Deployable vehicles Job i time window Figure 3.2:Illustration of the selection of an AGV to dispatch a job From the illustration in Figure 3.2, AGV3 is selected to dispatch job i since it has the least expected waiting time for the quay crane appointed time to unload or load job i from or to the vehicle. 3.2 DESIGN OF THE PMDS MODEL The planning of the time to dispatch each job is done in the following manner. The 1 st 4 jobs per crane will be assigned an appointed pickup/drop off time first. The fifth job per crane will be assigned when the service of the 1 st job at the quay has actually been completed. The assignment of the sixth job will depend on the completion of the 2 nd job and so on. The planning period is effectively 4 jobs ahead. For the 1 st appointed pick/drop off time of the i th job will be Appointed time = ship discharge time + (i-1) * time window 4 jobs, the For the next subsequent jobs after the 1 st four, the appointed pickup/drop off time of the j th job will be Appointed time = (j-4) th actual pickup/drop off time + 4* time window

21 Chapter 3 Current Deployment Scheme 21 Thus, for each crane, there are only 4 jobs at each time that are assigned an appointed pickup/drop off time. The assignment of the appointed pickup/drop off time for 8 jobs is illustrated with an example in Figure time 12:00am 12:02am 12:04am 12:06am 1st job actual pickup time 12:01am 12:02am 12:04am 12:06am 12:09am 2nd job actual pickup/drop off :02am 12:04am 12:06am 12:10am time 3rd job actual pickup/drop off time 12:03am 12:06am 12:11am 4th job actual pickup/drop off 4 12:05am 8 12:13am time Figure 3.3:An example of the assignment of the appointed pickup/drop off time for 8 jobs Before calculating the expected waiting time, the status of the AGVs must be determined. AGVs can be in the following 4 states, retrieving, delivering, going to park and idle or parked status. Only AGVs that are neither in the state of retrieving the next load nor being assigned to the next load are deployed in the current deployment scheme, PMDS. The waiting time for job L i, for the remaining 3 states of the AGV is calculated as follows: If the job L i is a u job, 1. If the AGV is delivering the current job, L j, Distance traveled by AGV, Dist = distance(agv current position, Lj destination) + distance(l j destination, L i source) Waiting time for L i = L i appointed pickup time (Dist/Average Velocity + crane average operating rate for Lj)

22 Chapter 3 Current Deployment Scheme If the AGV is going to park, going towards its assigned park location, Distance traveled by AGV, Dist = distance(agv current position, AGV destination) + distance(agv destination, L i source) Waiting time for L i = L i appointed pickup time Dist/Average Velocity 3. If the AGV is idle, Distance traveled by AGV, Dist = distance(agv current position, L i source) Waiting time for L i = L i appointed pickup time Dist/Average Velocity If the job L i is a l job, the value of Dist will be increased by another distance(l i source, L i destination). Moreover, the waiting time will be decremented by another yard crane average operating rate for Li. The whole deployment scheme can be visualized in Figure 3.4. For job L j AGV 0 AGV 1 AGV m Vehicle list AGV k AGV k+1... Pre-Calculation AGV j Deployable Vehicle list Select vehicle with minimum waiting time Job L j Assigned AGV m Figure 3.4:A visualization of the current deployment scheme The determination of the average velocity of each AGV is important since it is the only parameter that will affect the time information. The average velocity will be determined based on the historical statistical data information. This will be elaborated in Chapter 6.

23 Chapter 4 Proposed Deployment Scheme 23 4 PROPOSED DEPLOYMENT SCHEME The proposed deployment scheme can be formulated as a minimum cost flow problem (MCF) and solved with the network simplex algorithm. The network simplex code is written in C++ language and is easily available on the Web [13]. In this chapter, the formulation of the deployment of jobs as a minimum cost flow problem and the design of the model is discussed. 4.1 PROBLEM FORMULATION OF THE PROPOSED DEPLOYMENT SCHEME The containers to be served and the AGVs to be deployed can be formulated as nodes in the network. Assume in this problem, there are m number of AGVs and n number of containers or jobs. Altogether, there are a total of m+2n+1 nodes. The m AGV nodes can be regarded as source nodes and there is 1 sink node. Each container node will be split into 1 container node and 1 virtual container node (or container node) giving 2n container nodes as the transshipment nodes. The reason for splitting each container node into two is to ensure a flow through the node, i.e. a vehicle must pickup the container. This will be explained in the following. Given a network G (N, A), where N is a set of nodes and A is a set of arcs. The following needs to be defined before forming the network. N = {N AGV N JOB N JOB N S }. The set of nodes, N is split into 4 mutually exclusive set of nodes where NAGV is the set of m number of AGV nodes; NJOB is the set of n number of container nodes; N JOB is the set of n number of virtual container nodes and N S is the set of one sink node. The labeling of the nodes in each set is given as follows: o N AGV = {1,2,, m} o N JOB = {m+1, m+2,, m+n}

24 Chapter 4 Proposed Deployment Scheme 24 o NJOB = {m+n+1, m+n+2,, m+2n}. The m+1 node in NJOB corresponds to m+n+1 node in NJOB, and m+2 node corresponds to m+n+2 node and so on. o N S = {m+2n+1} A = {AJJ A\ AJJ }. Similarly, the set of arcs, A is split into 2 mutually exclusive set of arcs where AJJ is the set of arcs flowing between container node, NJOB to its corresponding container node, N JOB and A\ A JJ will simply be the set of the remaining arcs that excludes arcs in A JJ. o AJJ = {(i, j) A i NJOB, k, j NJOB, k, k = 1,2,,n}. NJOB, k and NJOB, k refers to the k th element in the set of NJOB and NJOB respectively. Thus, the mathematical formulation is as follows: (N1) subject to minimize c ij f ij j N j N AGV JOB f ij UN f S ji UN JOB ' f ( i, j) A = 1, = m, = ij ji ( i, j) A ( j, i) A f i N i N AGV S (1) (2), i N U N (3) JOB JOB' f ij = (4) 1, ( i, j) AJJ ' 0 fij 1, ( i, j) A \ AJJ ' (5) Alternatively, the problem can be formulated mathematically as: (N2) subject to minimize c ij f ij j N j N AGV JOB ( i, j) A f ij UN f S ji UN ij ( i, j) A\ A ( j, i) A JJ ' f f JOB ' f JJ ' ij ji ( i, j) A ( j, i) A\ A JJ ' f JJ ' ji = 1, = m, = 1, = 1, i N i N AGV S i N i N JOB' JOB (6) (7) (8) (9) f ij = (10) 0, ( i, j) AJJ ' 0 fij 1, ( i, j) A \ AJJ ' (11)

25 Chapter 4 Proposed Deployment Scheme 25 Both (N1) and (N2) formulations are similar except for equation (3) and (4) in (N1) is replaced by equation (8,9) and (10) respectively in (N2). The equation (4) in (N1) will ensure the container i be picked up by the AGV since the flow is one. In (N2), this constraint is satisfied by transforming into equation (8) and equation (9) where each container i is a sink node and virtual container i is the source node. Take note that the arc costs for arcs (i, j) A JJ and for arcs (i, j) A\A JJ, i N\N S and j N S are equal to zero since container i and j belongs to the same container and for vehicles to end at final destination after pickup respectively. An example for both formulations is illustrated below. Assume there are 2 AGVs to be deployed and 4 container jobs to be served. Thus, N AGV = {1,2} NJOB = {3,4,5,6} NJOB = {7,8,9,10} N S = {11} A JJ = {(i,j) A i N JOB, k, j N JOB, k, k = 1,4} The shaded nodes are the AGV nodes. An example of the network based on the formulation in (N1) and an example of the network based on the formulation in (N2) are illustrated in Figure 4.1 and Figure 4.2 respectively. The numbers in brackets indicate the lower and upper capacity of the arc flows in A JJ c (0,0) c (0,0) c 14 c 85 c c (0,0) (0,0) c 26 Figure 4.1:Example of a network of 2 AGVs and 4 containers using formulation (N1) 0 0

26 Chapter 4 Proposed Deployment Scheme 26 Figure 4.2:Example of a network of 2 AGVs and 4 containers using formulation (N2) However, only the formulation of the minimum cost flow problem in (N2) can be solved by the network simplex code used because it does not allow the lower capacity of the arcs to be set arbitrarily and not fixed at 0. The possible reason could due to a faster solving time for the network simplex code since the code is designed in that manner so that it is faster to solve without conversion of lower capacity to zero. The non-zero cost for each arc is determined in the following section Calculation of Non-zero Arc Costs Each container has two types of job movements as mentioned in Chapter 3, either an unloading or loading job. The issue here is whether the u job can be picked up in the quayside at the appointed time or the l job can be drop off in the quayside at the appointed time since the time of the job arrival in the quayside is crucial. Based on the idea of the waiting time from the current deployment scheme, PMDS, each arc cost can be thought of as the value of the time difference between the next job s appointed pickup/drop off time at the quayside to the current job s appointed time in the quayside plus some travel time; or the time difference between the next job appointed pickup/drop off time in the quayside to the current AGV ready time plus some travel time. To elaborate further, the calculation of the arc costs can be split into 2 sections: arc cost between an AGV node and the next job/container i node and arc cost between job i node and the job j node. The calculation of the arc costs and the term vehicle ready time will be elaborated further in the next section.

27 Chapter 4 Proposed Deployment Scheme Arc cost of arcs flowing from AGV to container node As mentioned, the job s pickup location is denoted as the source of the container to be loaded onto the AGV and the job s drop off location is denoted as the destination of the container to be unloaded from the vehicle. In addition, the time at which the vehicle is ready to be deployed is denoted as the vehicle ready time. Given that the job s source and destination are known and the AGVs positions can be monitored at all times, the vehicle ready time can be calculated. Each AGV can be in the following 4 states. Based on the status of the vehicle and the information given above, each vehicle s ready time can be calculated as follows: 1. If the AGV is in the state of retrieving the next job, L j at current time, AGV expected total distance travel, Dist = distance(agv current position, L j source) + distance(lj source, Lj destination) AGV ready time = current time + Dist/ Average velocity + Crane operating time rate at L j source + Crane operating time rate at L j destination 2. If the AGV is in the state of delivering the job, L i it carries at current time, AGV expected total distance travel, Dist = distance(agv current position, Li destination) AGV ready time = current time + Dist/ Average velocity + Crane operating time rate at Li destination 3. If the AGV is in the state of going to park at some location at current time, AGV expected total distance travel, Dist = distance(agv current position, AGV destination) AGV ready time = current time + Dist/Average velocity 4. If the AGV is in the state of idleness or remain at its current position at current time, AGV ready time = current time If the jobs L j and L i are u jobs, the crane-operating rate at the source is the quay crane-operating rate; otherwise the crane-operating rate at the destination is the yard crane-operating rate.

28 Chapter 4 Proposed Deployment Scheme 28 The arc cost from the AGV node to the container/job node is ready to be determined. There are 2 cases to this situation 1. If the next job, L j is a u job, Dist = distance(agv final destination, L j source) Arc cost = Lj appointed pickup time at quay (AGV ready time + Dist/Average Velocity) 2. If the next job, L j is a l job, Dist = distance(agv final destination, L j source) + distance(l j source, L j destination) Arc cost = L j appointed drop off time at quay (AGV ready time + Dist/Average Velocity + yard crane average operating time rate for L j ) The AGV final destination will be the expected destination of the next or current job served if it is in the state of retrieving or delivering at the current time respectively; or the expected destination of its park location or current position if it is in the state of going to park or idle at the current time respectively Arc cost of arcs flowing from container i to container j node The calculation of the arc costs from one container to another container node is slightly different from the calculation of the arc costs from an AGV to a container node. Since a job can be either a u or l job, there are 4 cases to this situation. 1. If L i is a u job and L j is a l job, Dist = distance(l i source, L i destination) + distance(l i destination, L j source) + distance(lj source, Lj destination) Arc cost = L j appointed drop off time at quay (L i appointed pickup time + Dist/Average velocity + yard crane average operating rate for L i and + yard crane operating rate for L j ) 2. If Li is a u job and Lj is a u job, Dist = distance(l i source, L i destination) + distance(l i destination, L j source) Arc cost = L j appointed pickup time at quay (L i appointed pickup time + Dist/Average velocity + yard crane average operating rate for Li) 3. If Li is a l job and Lj is a l job, Dist = distance(l i destination, L j source) + distance(l j source, L j destination)

29 Chapter 4 Proposed Deployment Scheme 29 Arc cost = Lj appointed drop off time at quay (Li appointed drop off time + Dist/Average velocity + yard crane average operating rate for Lj) 4. If L i is a l job and L j is a u job, Dist = distance(l i destination, L j source) Arc cost = Lj appointed drop off time at quay (Li appointed drop off time + Dist/Average velocity) The distance traveled or the 4 cases are illustrated in Figure 4.3. job L i source job L j destination job L i source job L j source QUAYSIDE d1 d3 d1 d2 d2 YARDSIDE job L i destination job L j source job L i destination Case 1: L i "u" job, L j "l" job Dist = d1 + d2 + d3 Case 2: L i "u" job, L j "u" job Dist = d1 + d2 job L i destination job L j destination job L i destination job L j source QUAYSIDE d1 d1 d2 job L j source Case 3: L i "l" job, L j "l" job Dist = d1 + d2 YARDSIDE Case 4: L i "l" job, L j "u" job Dist = d1 Figure 4.3:Illustration of the calculation of the distance traveled for the 4 cases It is possible that there is a negative arc cost value. For negative arc cost value between the two nodes, it means that the AGV that flows through this node is late for the job appointed time in the quay or the AGV can serve job i but will be late for the next job j. Thus, a large positive penalty cost will be assigned for flow on this arc to

30 Chapter 4 Proposed Deployment Scheme 30 allow some lateness for the AGV to pickup the job to safeguard against insufficient resources (AGVs). 4.2 DESIGN OF THE PROPOSED DEPLOYMENT SCHEME MODEL There will be varying number of containers at different points in time of the simulation. All incoming and unassigned containers at different points in time will be inserted into a queue based on the job appointed time in the quayside on First-in First out basis (FIFO) basis. We denote this queue as Q1. All the jobs in the queue and all AGVs will be formulated in the network based on formulation in (N2). All these information will be written into an input file and this will be solved by the network simplex code used for solving minimum cost flow (MCF) problem and the solution will be written to an output file. The jobs that are assigned to vehicles by the solution will be taken out of the queue, Q1. It is not practical to assign all the jobs based on the solution given because of the uncertainty of the traffic conditions. Some of the jobs could be late and this lateness will affect the rest of the later jobs exponentially. Moreover, the solution might not be optimal due to the change of the job status. Thus, re-planning needs to be done and the simulation needs to be halted temporarily after some jobs have been deployed at some point in time. Before actual deployment, all incoming containers will be assigned initially with an appointed pickup/drop off time. The time interval between jobs will be a constant time interval dictated by the length of time window. After replanning, the rest of the later un-deployed jobs will be assigned a new appointed pickup/drop off time based on the same time window interval from the 1 st un-deployed job. The new appointed time of the 1 st un-deployed job will be determined by the actual service time of the last job at the quayside with a grace period of 4 minutes. For each crane, the re-planning will be done after every k number of jobs have been deployed. After every k jobs for all cranes have been deployed, the MCF problem will be formulated based on the number of jobs remaining in the queue and the number of AGVs and resolved again based on new information. The number k depends on when the re-planning should be done based on historical traffic condition.

31 Chapter 4 Proposed Deployment Scheme 31 Following the pmds model, k is selected to be 4. An example of assignment of the appointed time sequence for 10 jobs for a single crane is illustrated in Figure 4.4. Another aspect of the model encountered is that there are always lesser resources (AGVs) compared to the number of jobs waiting to be serviced. Thus, it is possible that there is more than one job assigned to an AGV. In order to handle this, there will be a queue of jobs assigned to each AGV. The job queue for each AGV is also based on FIFO and the AGV will perform the earliest assigned job. The job that is serviced by this AGV will be removed from the Q1 but the remaining jobs in the job queue for the AGV will remain in the Q1 either waiting to be serviced or reformulated and solved by MCF code. Thus, it is possible that the later assigned jobs in the job queue for AGV i will be re-assigned to the job queue for AGV j based on the solution from MCF. Initially job time 12:00 am12:02am12:04am12:06am12:08am12:10am12:12am12:14am12:16am 12:18am reformulation & solve After 1st deployment of first 4 jobs expected appointed time job time 12:08am 12:12am12:14am12:16am12:18am12:20am12:22am job 4 actual service time reformulation & solve After 2nd deployment of next 4 jobs job time 12:17am 12:21am12:23am job 8 actual service time Figure 4.4: An assignment example of appointed time for 10 jobs for 1 crane From the example in Figure 4.4, the initial assigned appointed pickup/drop off time of each job at the quayside will start from 12:00am to 12:18am at intervals of 2 minutes of time window each. After the deployment of the 1 st 4 jobs, the last job of the batch,

32 Chapter 4 Proposed Deployment Scheme 32 i.e. job 4 is found to be picked up or drop off at 12:08am, 2 minutes behind the appointed time at 12:06am. Thus, the job 5 to 10 will be re-assigned from 12:12am to 12:22am. After the deployment of the next 4 jobs, the last job of the batch, i.e. job 8 is found to be picked up or drop off at 12:17, 1 minute earlier from the appointed time at 12:18am. Thus, job 9 to 10 will be re-assigned 12:21am to 12:23am.

33 Chapter 5 Deadlock Prediction and Avoidance Algorithm 33 5 DEADLOCK PREDICTION & AVOIDANCE ALGORITHM Since both deployment schemes make use of the deadlock prediction and avoidance algorithm, it is necessary to discuss the algorithm used. A system is said to be in a deadlock if a part or the whole of the system stalls. In the AGVS, resources (zones between control points) are shared among the whole population of vehicles. Each of the vehicles can only occupy one zone at a time. Such maintenance of control over particular resources (zones) allocated to a vehicle may bring about deadlock (see Figure 5.1) In this chapter, the necessary conditions leading to deadlock, the different types of deadlock that can be deduced from the routing policy of the AGVS and the deadlock prediction and avoidance measures take will be discussed based on a study by Wee and Moorthy[1]. Zone1 Zone4 Zone2 Zone3 Figure 5.1:A cyclic deadlock formed by the vehicles 5.1 THE CONDITIONS LEADING TO A DEADLOCK From Coffman, Elphick and Shoshani [4], the four conditions that must be satisfied are as follows:

34 Chapter 5 Deadlock Prediction and Avoidance Algorithm 34 Mutual exclusion: 2 or more processes cannot use a resource at a time No preemption: When a resource is being used, it is not released until the process using it finishes with it. Hold and wait: A process that is holding at least one resource and is waiting to acquire additional resources that are currently being seized by other processes. Circular wait: A closed chain of processes in which each process is waiting for a resource occupied by next process in the chain Thus, a deadlock will not occur if one of the conditions does not hold. For AGVS, the 1 st three conditions are always true and only the last condition can be prevented. The resources mentioned in the four conditions refer to zones of the path and the processes refer to the AGVS. Mutual exclusion is obvious since two vehicles cannot occupy a zone at the same time. This is a condition required by the control system to prevent two vehicles from colliding with each other. No preemption is also obvious because, the vehicle must be in any zone at a given time and the movement of the vehicle into another zone satisfies the condition. As for the Hold and Wait condition, it is also satisfied in the case of the AGVS, as each vehicle has to be in a zone at any one time and is waiting to move into its next designated zone. The last condition, Circular Wait is not always true in AGVS and this is where the deadlock prediction can be used to detect whether a deadlock is imminent. 5.2 TYPES OF DEADLOCK IN THE AGVS Given the layout of the routes traveled by the vehicles, the three most common kinds of deadlock encountered by the vehicles are the cross lane deadlock, shop deadlock and cyclic deadlock. The description of these deadlocks is presented in [1]. Cross lane deadlock can be resolved by engineering a smarter navigation system to control the vehicles especially deciding the appropriate distance to stop and wait before switching to the other lanes. Shop deadlock is minimized through PSA distribution algorithm that assures the space constraint is not tight. Cyclic deadlock is the most generic and shown in Figure 5.1 where there is a chain of vehicles requesting for the zones (resources) in such a way that these form a cyclic request of zones. The prediction and avoidance algorithm is designed to counter this last situation.

35 Chapter 5 Deadlock Prediction and Avoidance Algorithm METHODS IN PREDICTING OR DETECTING CYCLIC DEADLOCK Due to the small sample time, in the range of 1.5 to 2 seconds, for the control system, the computation time to predict the cyclic deadlock must be small. The methods described in the literature in [5,6,7,8] in predicting this deadlock are either complicated or computationally expensive. A brief description of the reason why these methods are not appropriate is presented in the following. In [5,6], Lee, Lin and Viswanadham, Narahari and Johnson use the petri-net theory to predict deadlock in the MHS and AGVS. The entire network must be presented in the form of matrix. However, the implementation of the AGVS layout will consist of 1370 nodes and several thousand arcs. Thus, the dimension of the matrix is in the order of millions and a lot of memory space is taken out. Matrix-vector operation needs to be done to detect a cyclic deadlock. The computation per iteration is in O(mn) where n is the number of nodes and m is the number of arcs of the network. Thus, this method is not feasible. In [7], Hyuenbo, Cho, Kumaran and Wysk use graph theory to detect impending deadlock. In order to do that, bounded circuits defined in [8] have to be found. However, the number of bounded circuits of the network of AGVS is very large due to its complexity and hence this method is also dropped. 5.4 PROPOSED DEADLOCK PREDICTION STRATEGY Due to the unavailability of fast methods of predicting deadlock in the literature, Wee and Moorthy[1] proposed a new approach to predict deadlock. The algorithm for the proposed one-zone step deadlock prediction is presented as follows: The definition of the numbers in Figure 5.2 is listed as follows: 1. Extract the location (L p ) (or control points) of its next zone of the selected vehicle (say Vi) that is about to enter a new zone. For every sampling time in the control system, i.e. 1.5 sec to 2 sec, a check is done to see if a vehicle has moved to a new zone or not. If it has, the vehicle is selected so that a deadlock prediction for its next zone step is done

36 Chapter 5 Deadlock Prediction and Avoidance Algorithm Check whether this next zone (Lp) is occupied by another vehicle 3. Extract the location (Lq) of Vi s next 2 zone (i.e. the next next zone) 4. Check whether any other vehicle occupies L q 5. Extract next zone location (L r ) of the vehicle that is occupying L q and update Lq to the location Lr 6. Return vehicle is waiting for the block to clear 7. Return vehicle is safe to proceed, deadlock is not predicted 8. Check whether L p is equal to L q 9. Return vehicle is not safe to proceed, deadlock is predicted 1 Occupied? 2 Yes 6 No 3 Occupied? 4 No 7 Yes No 5 8 Equal? Yes 9 An example: Figure 5.2:Flowchart of the one-zone step deadlock prediction algorithm 1 AGV 1 2 AGV1's "next next" location AGV AGV 2 4 AGV 3 Figure 5.3: Illustration of one-zone step deadlock prediction

37 Chapter 5 Deadlock Prediction and Avoidance Algorithm 37 The example in Figure 5.3 illustrates 4 vehicles AGV1 to AGV 4 and the shaded nodes are the locations of the vehicles. The arcs in each of these nodes are pointing to the next location node of the vehicle s route. For example, AGV4 s next location will be node 2. Following the given algorithm for the one zone step deadlock prediction, say AGV1 is about to enter a new zone i.e. node 2. It checks whether node 2 is occupied (Here, the node is free). It then checks its next next node, which is node 3. It finds that AGV2 is occupying the node and hence, AGV2 s next node is checked, which is node 4. AGV3 is found to be occupying node 4 and then it continues to check AGV3 s next node i.e. node 5 and finds that AGV4 is occupying it. Finally it checks that AGV4 s next node i.e. node 2 is the same node that AGV1 wants to enter to. If AGV1 is allowed to enter 2, there will be a cyclic request of resources, which implies a cyclic request of resources and hence cyclic deadlock. The algorithm will thus return a value saying that a deadlock is predicted at the next zone step. The computational complexity of the algorithm in the worst case is O(V 2 ) where V is the number of vehicles in the entire AGV system. This worst case occurs when the entire fleet of vehicles forms a huge cyclic deadlock. In a control system, it will be difficult to detect when an AGV exactly enters new zone i.e. just crosses the boundary line of the previous zone and the new zone. This is due to the reason that the data is sent to the central control system in every sampling time of 1.5 seconds such that the detection of crossing a zone boundary exactly cannot be detected. In order to detect whether the vehicle has entered a new zone, a comparison of the previous sampled position and the newly sampled position of the vehicle is done. If there is a change in the zone, the vehicle has entered a new zone. Here, it is assumed that a vehicle cannot traverse an entire zone within 1.5 seconds. It is possible to extend this idea of one-zone step to the two-zone step prediction to facilitate a better performance by predicting the deadlock earlier. However, there is a disadvantage of this form of prediction in the implementation as mild approximations are done here. These kinds of approximations come into effect because the vehicles do not travel from one point to another in exactly the theoretical time required. This difference between the expected time and the actual time creates an error. This error of prediction gets larger as more zone steps are predicted in advance. Thus, it is

38 Chapter 5 Deadlock Prediction and Avoidance Algorithm 38 sufficient to use one-zone step prediction and implement the necessary deadlock avoidance strategy mentioned in the next section 5.5 PROPOSED DEADLOCK AVOIDANCE STRATEGY Normally, there are two ways to resolve deadlock: detection-resolution and prediction-avoidance. The prediction-avoidance strategy is used since this strategy will minimize the number of formation of deadlocks. To further minimize the deadlock formation, Wee [1] has implemented a one-zone step resolution to resolve the deadlock, which will be explained later. The two strategies used in the avoidance measure consist of: Wait and Proceed As the name suggests, if a vehicle predicts a deadlock in its route, it will stop and wait at the same location until at least one vehicle is cleared from the deadlock prediction region Rerouting Due to the time constraints, a semi-dynamic routing strategy instead of dynamic routing strategy is proposed. To facilitate deadlock prediction and avoidance, a set of static route for each AGV is ascertained before moving to the destination. The routes are stored in a table and when an AGV requests for its next location, the next zone or location is returned for the particular requesting AGV. Thus, every AGV will follow its ascertained route from the stored information at one control point or location at a time. The semi-dynamic rerouting strategy comes to play, and routes need to be recalculated when one of the conditions holds: The AGV reaches the destination and picks up a new job and is ready to move to the job s destination. The AGV reaches the destination and drops off a job and is ready to move to the next job s pickup location. The deadlock prediction algorithm predicts the formation of a deadlock in the next location or a new zone and requests for a new route for the AGV.

39 Chapter 5 Deadlock Prediction and Avoidance Algorithm 39 It is not necessary for the routing strategy to be dynamic since it is costly and moreover, the deadlock formation is not very frequent. The route is calculated using the Dijkstra s algorithm to find the shortest path tree (SPT). The general outline of the Dijkstra s algorithm and the implementation are explained in detail by Ahuja, Magnanti and Orlin [9] and Gallo [10]. The performance of the shortest path algorithms is dependent on the network and there are a lot of variants of the shortest path algorithms specific to the underlying network One-zone step deadlock resolution A one-zone step deadlock resolution strategy acts as an enhancement to the prevention-avoidance measure discussed before since deadlocks can still form. Deadlocks can form due to the uncertainty of traffic especially from the loading and unloading effects. Thus, deadlock resolution is implemented at the quay and yard side where loading and unloading occurs. The resolution algorithm will assign a virtual intermediate control point to the AGV when deadlock occurs at the quay or yard side during loading/unloading operations. After completion of the loading/unloading process, this AGV is prepared to move on to its new destination. If it encounters a cyclic deadlock meaning there is a cyclic request of their next control points by other AGVS, this particular AGV will reroute to this virtual location that will break the cyclic request. Otherwise, this AGV will follow the pre-assigned shortest route.

40 Chapter 6 Implementation 40 6 IMPLEMENTATION In this chapter, a description of the simulation software, AutoMod and some of the preparation steps taken before the simulation is provided. 6.1 AUTOMOD SIMULATION SOFTWARE AutoMod software is used for discrete-event system simulation. In discrete-event simulation, a system is modeled in terms of its state at each point in time; the entities that pass through the system and the entities that represent system resources; and the activities and events that cause system state to change. Discrete-event models are appropriate for those systems for which changes in system state occur only at discrete points in time. It offers a complete environment for user to define scenarios, conduct experimentation and performs analyses to models built in AutoMod and includes other software packages such as AutoView to do the 3-dimension animation and AutoStat to do a statistical analysis of the model. 6.2 SPECIFICATIONS OF THE TWO MODELS The model for current deployment scheme is termed as pmds model and the model for the proposed deployment scheme is termed as mcf model. In this project, a simplified specification is used to model and simulate the actual workload for the two different models. Both models use the same specifications. The specifications are as follows: Each vehicle is assumed to be able to ferry only a unit load from quay to yard side or vice versa at any point in time. The service time interval is deterministic and the re-assignment of the service time will be done based on the methods in section 3.2 and 4.2. A berth is randomly assigned to an incoming ship. If the berths are full, the next incoming ship will wait in the queue until the previous ship has completed discharging/unloading.

41 Chapter 6 Implementation 41 The arrival of the ship is assumed to follow an exponential distribution of mean 60 minutes. This means the arrival rate for each ship follows an exponential distribution where 63% of the time the arrival rate is less than 60 minutes and 37% of the time the arrival rate is more than 60 minutes. Each container storage yard is made up of 9 clusters. Each cluster is made up of 3 control points. At any one time, a single cluster can only be used by a quay crane for either discharging or loading process. It is possible to move the quay cranes but the movement is not simulated here. 4 quay cranes are assigned per vessel. The distribution of workload of each quay crane is as follows: 1 st quay crane: 18% 2 nd quay crane: 25% 3 rd quay crane: 27% 4 th quay crane: 30% The time taken for a quay crane to load and unload a container follows a triangular distribution of (1.375, 1.708, 2.113) minutes. The time taken for a bridge crane to load and unload a container follows a triangular distribution of (1.593, 2.172, 2.728) minutes The crane average operating rate required for the calculation in Chapter 3 and 4 is taken to be the average of the 3 given values of the triangular distribution illustrated above. Before embarking on the simulation, some preparations need to be done. 6.3 DETERMINATION OF THE EXPECTED VALUES OF AVERAGE VELOCITY OF THE VEHICLES The determination of the average velocity for each AGV is important, as it will affect the calculation of the expected traveling time it needs from one location point to the other location point. The way to ensure that the value of the average velocity is realistically determined is to collect the values of the AGVs average velocities by running the simulation model a few times before the actual simulation for different number of AGVs takes place. It is not possible to list out all the average velocities

42 Chapter 6 Implementation 42 traveled by the AGVs in this report. Only the average velocities in meters per second for any 10 AGVs out of total number of AGVs used in the 2 simulation models will be listed in Table 6.1. Pmds model Mcf model 40 AGVs 60 AGVs 80 AGVs 40 AGVs 60 AGVs 80 AGVs Mean SD. Mean SD. Mean SD. Mean SD. Mean SD. Mean SD Table 6.1: List of average velocities of random selection of 10 AGVs Alternatively, the average velocity for all AGVs can be calculated as a single number instead since the variation of the average velocities of each AGV for each case in the model is small. The total average velocity in meters per second for the total number of AGVs used in the 2 simulation models will be listed in Table 6.2 Pmds model Mcf model 40 AGVs 60 AGVs 80 AGVs 40 AGVs 60 AGVs 80 AGVs Mean SD. Mean SD. Mean SD. Mean SD. Mean SD. Mean SD Table 6.2:Average velocity for the total number of AGVs used To make a fair comparison, the lower average velocity values of the two models are chosen and entered into the two simulation models before the actual simulation. 6.4 C-CODES AND INTERFACING The mcf model needs to interface the AutoMod simulation model with the MCF solver in order to form and solve the network. As AutoMod simulation language is only able to support C and not C++ platform and the given MCF code is in C++ platform, a C function has to be written in AutoMod to call up the executable version of MCF code to solve the network. Similarly, a C function has to be written to write the arc values and nodes to an input file based on the format stated in Appendix A. The optimal solution from MCF will only give the feasible flows in the network. Thus, a C function needs to be written to trace the jobs serviced by each AGV in the

43 Chapter 6 Implementation 43 order from the first to the last job and output the information to a file. A C function has to be written again in AutoMod to read the file and store this information to the simulation model. The interface between the C function and AutoMod for the mcf model is shown in Figure 6.1 Automod model 1. call up C func. network formulation Input file 3. input 2. call up C func. call up MCF solver input Output file generate C func. trace the arc flow generate Output file Figure 6.1: Illustration of the C interface with the AutoMod model for the mcf model

44 Chapter 7 Results and Discussions 44 7 RESULTS AND DISCUSSION Both the current deployment and proposed deployment schemes together with the one-zone step deadlock prediction and avoidance algorithm are implemented in the model based on the specifications mentioned in section 6.2. Both the pmds model and mcf model layouts consist of four berths and varying number of AGVs ranging from 40 to 80. The main objective of this project is to compare the performance of the mcf model against the pmds model. 7.1 SCHEMATICS OF THE SIMULATION MODEL LAYOUT The layout of the four berths used in the simulation of the two models is shown in Figure 7.1. A scenario showing the AGVs waiting to pick up or drop off container jobs on the berth side and container storage area in the yard side can be shown in Figure 7.2. Figure 7.1: Layout of the four berths in the simulation model AGVs picking/dropping load in the yard side AGVs picking/dropping load in the berth side Figure 7.2:Scenarios showing AGVs picking/dropping jobs in the berth and yard areas